Disordered Perovskite BaCu1/3Ta2/3O3

• Disordered Perovskite BaCu1/3Ta2/3O3 is a quantum magnet where randomly distributed Cu²⁺ and Ta⁵⁺ ions create a bounded exchange interaction spectrum leading to a dynamic singlet state.
• Synchrotron XRD and XAS analyses confirm a predominantly tetragonal lattice with Jahn–Teller distorted CuO₆ octahedra and nearly regular TaO₆, highlighting significant local chemical ordering.
• Magnetic measurements and the distributed-exchange dimer plus orphan model reveal no long-range order, a finite-randomness regime, and substantial residual magnetic entropy at low temperatures.

BaCu$_{1/3}$Ta$_{2/3}$O$_3$ (BCTO) is a three-dimensional disordered perovskite quantum magnet where magnetic Cu$^{2+}$ ($S = 1/2$) and non-magnetic Ta$^{5+}$ ions randomly occupy the B-sublattice of a pseudo-cubic ABO$_3$ unit cell in a 1:2 ratio. The random yet anti-clustered arrangement of B-site cations results in a structurally constrained distribution of magnetic exchange interactions. This scenario generates a quantum ground state composed of random spin singlets with a broad but bounded exchange spectrum, distinct from the conventional infinite-randomness fixed point associated with random-singlet phases (Mahapatra et al., 24 Jan 2026).

1. Crystallography and Local Structure

Synchrotron X-ray diffraction (XRD) analyses show that BCTO crystallizes predominantly in a tetragonal perovskite lattice (P4/mmm, with a minority P4mm phase), with $c/a \approx 1$. Ba$^{2+}$ exclusively occupies the A-site. In both phases, Cu$^{2+}$ and Ta$^{5+}$ ions are distributed randomly over the B-site, resulting in nearly linear B–O–B superexchange paths (bond angle $\approx$ 180°). The minority P4mm phase features a slight B-site off-centering, resulting in minor additional broadening of exchange couplings.

X-ray absorption spectroscopy (XAS) at the Cu K- and Ta L$_{III}$-edges confirms the formal valences of the transition-metal cations. Extended X-ray absorption fine structure (EXAFS) measurements reveal that CuO$_6$ octahedra are strongly Jahn–Teller distorted with four short Cu–O$_1$ bonds ($R_{\rm CuO_1}=2.03(1)$ Å) and two long Cu–O$_2$ bonds ($R_{\rm CuO_2}=2.32(1)$ Å), whereas TaO$_6$ octahedra are nearly regular ($R_{\rm TaO}=1.98(1)$ Å). Coordination statistics demonstrate significant local chemical ordering: each Cu on average is neighbored by about $N_{\rm Cu-Ta} \approx 5.6$ Ta ions and $N_{\rm Cu-Cu} \approx 0.4$ Cu ions at the next B-site shell; Ta sites have $N_{\rm Ta-Cu} \approx 2.9$ and $N_{\rm Ta-Ta} \approx 3.1$. This chemical short-range order suppresses extended Cu–O–Cu superexchange networks and thus large magnetic cluster formation (Mahapatra et al., 24 Jan 2026).

2. Magnetic Hamiltonian and Distribution of Exchange Interactions

At low temperatures, where no magnetic long-range order or spin freezing is observed down to 0.1 K, the effective low-energy physics is described by a random-bond spin-$1/2$ Heisenberg Hamiltonian,

$$H = \sum_{\langle i,j\rangle} J_{ij}\, \mathbf{S}_i \cdot \mathbf{S}_j - g\mu_B \sum_i \mathbf{H} \cdot \mathbf{S}_i,$$

where the sum runs over Cu–O–(Ta–O–)…–O–Cu exchange paths of varying length. The hetero-atomic local order and suppressed Cu clustering produce a broad yet intrinsically bounded distribution $P(J)$ of exchange constants, with multiple peaks corresponding to direct Cu–O–Cu, Cu–O–Ta–O–Cu (one intervening Ta), and longer exchange pathways involving two or more Ta ions.

The distribution $P(J)$ is empirically reconstructed from thermodynamic and magnetic data using a sum of log-normal components:

$$P(J) = \sum_{k=1}^K w_k \frac{1}{J\,\sigma_k \sqrt{2\pi}} \exp \left[-\frac{(\ln J - \ln J_{0k})^2}{2\sigma_k^2} \right], \quad \sum_k w_k = 1,$$

where $J_{0k}$, $\sigma_k$, and $w_k$ parameterize each log-normal peak, representing distinct exchange pathways. $P(J)$ remains finite as $J \to 0$, indicating the absence of truly vanishing exchange scales (Mahapatra et al., 24 Jan 2026).

3. Magnetic and Thermodynamic Properties

Magnetic susceptibility $\chi(T)$ measured at fields $0.1$–$9$ T exhibits no evidence of long-range magnetic ordering or spin freezing down to $0.1$ K. At $T \gtrsim 50$ K, a Curie–Weiss fit gives an effective moment $\mu_{\rm eff} = 1.85(5)\,\mu_B$ and Weiss temperature $\theta_{\rm CW} = -35(10)\,$K—consistent with isolated Cu$^{2+}$ spins coupled antiferromagnetically. Below $10$ K, $\chi(T)$ displays a weak power-law divergence, $\chi(T) \propto T^{-\gamma}$, with $\gamma \approx 0.67$ in the range $4\,{\rm K} \gtrsim T \gtrsim 1\,{\rm K}$, and $M[H,T]$–scaling is observed for both susceptibility and isothermal magnetization $M(H)$, characteristic of systems with a broad distribution of energy scales.

Heat-capacity measurements $c_p(T, H)$ down to $0.1$ K reveal a broad Schottky-like anomaly. After subtracting the phonon contribution, the magnetic specific heat $c_{\rm mag}/T$ deviates from the $T^{-(1-\gamma)}$ prediction of the infinite-randomness random-singlet scenario. Instead, for $T \ll 1$ K, $c_{\rm mag}(T) \propto T$ (a Sommerfeld-like linear term) and scaling is absent. Integration of $c_{\rm mag}/T$ from $0.1$ to $20$ K yields a recovered entropy $\Delta S_{\rm mag} \approx 0.4\,R\ln2$, indicating 60% of Cu spins remain dynamic at the lowest measured temperature (Mahapatra et al., 24 Jan 2026).

4. Distributed-Exchange Dimer plus Orphan Model

A combined quantitative fit to susceptibility, magnetization, and specific-heat data is achieved using a “distributed-exchange dimer plus orphan” model. In this description, a small fraction $f \approx 0.04$ of Cu spins act as free (orphan) monomers, while the majority form antiferromagnetic dimers whose exchange strength is drawn from the empirically reconstructed $P(J)$. The model employs standard expressions for the susceptibility and Schottky anomaly of $S=1/2$ dimers and monomers and achieves a global rms deviation $\lesssim 3\%$ across all magnetic field and temperature data sets.

This approach accommodates the residual Curie tail in $\chi(T)$, the linear-in-$T$ low-temperature specific heat, and the observed entropy recovery profile. The small orphan-spin fraction accounts for the nuclear Schottky contribution and matches the suppression of large-scale Cu–O–Cu networks indicated by local structure analysis (Mahapatra et al., 24 Jan 2026).

5. Ground State and Theoretical Implications

In many random quantum magnets, especially in one dimension or highly frustrated lattices, strong-disorder renormalization group (RSRG) theory predicts flow to an infinite-randomness fixed point, resulting in a scale-free singlet-bond distribution,

$$P_{\rm IRFP}(J) \propto J^{-\gamma}, \quad 0 < \gamma < 1,$$

along with thermodynamic singularities $\chi \propto T^{-\gamma}$ and $c_{\rm mag} \propto T^{1-\gamma}$. In contrast, in BCTO, the disorder is unfrustrated and constrained by the structural and chemical correlations between Cu and Ta ions. The consequence is a bounded $P(J)$, finite as $J \to 0$, with peaks near $0.1$ K (long exchange paths), $4$ K (paths with one Ta), and $70$ K (direct Cu–O–Cu). This prevents flow to an infinite-randomness fixed point.

At the lowest temperatures, the specific heat recovers to a linear $T$ dependence and scaling collapses in $c_p$ are lost, consistent with a finite-randomness regime. Approximately 60% of magnetic entropy remains unquenched at $0.1$ K, supporting the presence of a highly dynamic singlet network rather than a frozen or ordered state (Mahapatra et al., 24 Jan 2026).

6. Broader Context and Relevance

The results place BaCu$_{1/3}$Ta$_{2/3}$O$_3$ within a new category of three-dimensional quantum magnets in which "structurally constrained" randomness creates a broad yet bounded distribution of magnetic interactions. No magnetic ordering or spin freezing is found despite a Cu-site occupancy above the percolation threshold for the cubic lattice. The system provides an archetype for experimentally realizing a random quantum singlet ground state not governed by the infinite-randomness scenario, but by a finite-randomness RG flow. A plausible implication is the engineering of quantum spin liquid–like ground states via controlled disorder and cation ordering, providing an alternative to magnetic frustration as a route to quantum-disordered phases. This scenario may be relevant for other structurally disordered oxides and points to new experimental strategies for exploring three-dimensional disordered quantum magnetism (Mahapatra et al., 24 Jan 2026).